NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2: Introduction to Linear Polynomials by PW

Polynomials are an important part of Class 9 Maths, but identifying different types of polynomials, finding their degree and coefficients, and calculating their values can be challenging. Questions that involve forming algebraic expressions from everyday situations also require a clear understanding of these concepts and their applications.

Physics Wallah provides NCERT Solutions for Introduction to Linear Polynomials, covering important questions on polynomials, their degree, coefficients, values, and algebraic expressions. These solutions help you check your answers, clear doubts, and revise key concepts through practice.

Class 9 Maths Ganita Manjari Chapter 2 Solutions

Get clear solutions to important questions from Class 9 Maths Ganita Manjari Chapter 2, covering linear polynomials, their degree, coefficients, values, and algebraic expressions.

Lecture 01: Solving equations and Word problems

Lecture 01 covers polynomials, their degree, classification, coefficients, and constant terms. The selected questions below include the main concepts covered in the PDF.

Questions and Answers

Q1. Which of the following are polynomials?

(i) 3x² + 5x − 7
(ii) 1x + 4
(iii) 7y³ − 2y + 9
(iv) x + 5
(v) x² + 3x + 1

Answer: As marked in the PDF:

• (i) 3x² + 5x − 7 — Polynomial

• (ii) 1x + 4 — Not a polynomial

• (iii) 7y³ − 2y + 9 — Polynomial

• (iv) x + 5 — Not a polynomial

• (v) x² + 3x + 1 — Marked with a cross in the PDF.

Q2. Find the degree of each polynomial.

(i) 7y³ − 2x + 5
(ii) 4y³ + y² − 9
(iii) 9a − 6
(iv) 2m⁴ − 5m² + 7m − 1
(v) 8x⁵ − (3x⁵ + 2x³) − 5x⁵ + x² − 4

Answer:

• (i) Degree = 3

• (ii) Degree = 3

• (iii) Degree = 1

• (iv) Degree = 4

• (v) Simplifying gives −2x³ + x² − 4, so degree = 3.

Q3. Find the degrees of the following polynomials.

(i) 2x² − 5x + 3
(ii) y⁴ + 2y − 1
(iii) −9z⁰
(iv) 4z − 3

Answer:

• (i) 2

• (ii) 4

• (iii) 0

• (iv) 1

Q4. Classify the following polynomials.

(i) x − x³
(ii) y + y⁴ + 4
(iii) 2x − 1
(iv) 5x³
(v) 3
(vi) t²

Answer:

• (i) Cubic

• (ii) Quartic

• (iii) Linear

• (iv) Cubic

• (v) Constant

• (vi) Quadratic

Q5. Find the coefficients of x² and x in 7x² − 3x + 5.

Answer:

• Coefficient of x² = 7

• Coefficient of x = −3

Q6. Find the coefficients of a³ and a in −9a³ + 4a − 1.

Answer:

• Coefficient of a³ = −9

• Coefficient of a = 4

Q7. What are the coefficients of x² and x³ in x⁴ − 3x³ + 6x² − 2x + 7?

Answer:

• Coefficient of x² = 6

• Coefficient of x³ = −3

Q8. What is the coefficient of z in 4z³ + 5z² − 11 + 0z?

Answer: 0

Q9. What is the constant term of 9x³ + 5x² − 8x − 10?

Answer: −10

Q10. Write the following for the polynomial x³ + 2x + 35 − 72x² − x⁶.

(i) Degree of the polynomial
(ii) Coefficient of x³
(iii) Coefficient of x⁶
(iv) Constant term

Answer:

• Degree = 6

• Coefficient of x³ = 15

• Coefficient of x⁶ = −1

• Constant term = 35

Class 9 Maths Chapter 2 Solutions PDF

You can use this PDF to practise questions on solving equations and word problems.

Lecture 02: Linear Patterns

Lecture 02 covers the value of a polynomial and forming algebraic expressions from everyday situations. The questions include substitution, ages, costs, measurements, and quantities.

Questions and Answers

Q1. Write a polynomial of degree 3 in x in which the coefficient of the x² term is −7.

Answer: Examples given in the PDF include:

• 2x³ − 7x²

• −5x³ − 7x² + 2x + 3

Q2. Find the value of 5x − 3 when x = 2.

Solution:

5(2) − 3
= 10 − 3
= 7

Q3. Find the value of 2a² + 4a − 1 when a = −2.

Solution:

2(−2)² + 4(−2) − 1
= 8 − 8 − 1
= −1

Q4. Find the value of 3m³ − 2m² + m − 5 when m = 2.

Solution:

3(2)³ − 2(2)² + 2 − 5
= 24 − 8 + 2 − 5
= 13

Q5. Find the value of x⁴ − 3x³ + 2x² − x + 1 when x = −1.

Solution:

(−1)⁴ − 3(−1)³ + 2(−1)² − (−1) + 1
= 1 + 3 + 2 + 1 + 1
= 8

Q6. An online store sells one T-shirt for ₹500 and one cap for ₹250. Riya buys m T-shirts and n caps. The delivery charge is ₹100. Write an algebraic expression for the total bill.

Answer:

Total bill = 500m + 250n + 100

Q7. A team pays ₹50 as an entry fee per player and ₹300 for each jersey. If it buys x entry passes and y jerseys, write an algebraic expression for the total expense.

Answer:

Total expense = 50x + 300y

Q8. The length of a rectangle is x + 3 cm and its breadth is y − 2 cm. Write an algebraic expression for its perimeter.

Solution:

P = 2(l + b)

= 2(x + 3) + 2(y − 2)

= 2x + 6 + 2y − 4

= 2x + 2y + 2

Q9. A rectangular garden has length x metres and breadth 6 metres. The cost of fencing the length is ₹50 per metre and the breadth is ₹30 per metre. Write an algebraic expression for the total fencing cost.

Solution:

Cost of length = 2x × 50 = 100x

Cost of breadth = 2 × 6 × 30 = 360

Total cost = 100x + 360

Q10. A rectangular garden has length x metres and breadth x + 5 metres. Write an algebraic expression for its area.

Solution:

Area = l × b

= x(x + 5)

= x² + 5x

Class 9 Maths Chapter 2 Solutions PDF

You can use this PDF to practise linear patterns.

Additional Class 9 Maths Chapter 2 Solutions PDFs

Three additional Solutions PDFs from the Introduction to Linear Polynomials series are provided separately. Use them for effective exam preparation.

What Can You Learn from the NCERT Class 9 Maths Ganita Manjari Chapter 2 Solutions by PW?

The chapter Introduction to Linear Polynomials covers key algebraic concepts that can be challenging without enough practice. PW solutions help you understand these concepts through solved questions and examples.

• Identify Polynomials: Recognise polynomials and their different types.

• Find the Degree: Determine the degree of a polynomial.

• Understand Coefficients: Identify coefficients and constant terms.

• Evaluate Polynomials: Calculate polynomial values for given variables.

• Form Algebraic Expressions: Represent everyday situations using algebraic expressions.

• Revise Key Concepts: Check your answers and practise important questions.

Class 9 Maths Chapter 2 introduces polynomials and their use in algebraic expressions through concepts and practical examples. Practising questions on degree, coefficients, polynomial values, and expressions can strengthen your understanding. These solution PDFs provide a concise way to revise these concepts and practise important question types.